Subgroups — #18088056

Order 4864.

1350 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10597294	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926545	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926313	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561864	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#520	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	C₂×#10597294	—	2	2	no	—
13	C₂×#10597294	—	2	2	no	—
14	C₂×#10597294	C₄	1	4	yes	complemented
15	#11926545	—	2	2	no	—
16	#11926545	C₄	1	4	yes	complemented
17	C₂×#10597292	—	2	1	no	—
18	C₂×#10597289	—	2	1	no	—
19	C₂×C₁₉⋊#95	—	2	2	no	—
20	#11926313	—	2	2	no	—
21	#11926306	—	2	1	no	—
22	#11926306	—	2	1	no	—
23	#11926303	—	2	2	no	—
24	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#520	—	2	2	no	—
26	C₁₉×#520	—	2	2	no	—
27	C₁₉×#520	—	2	2	no	—
28	C₁₉×#520	C₄	1	4	yes	complemented
29	C₂×C₄×Q₈×C₁₉	—	2	1	no	—
30	C₂×C₄×D₄×C₁₉	—	2	1	no	—
31	C₂×C₄×D₄×C₁₉	—	2	2	no	—
32	C₂×C₁₉×#117	—	2	1	no	—
33	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
36	C₂×#41×C₁₉	—	2	1	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	—	2	1	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
43	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
44	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
45	C₂×#41×C₁₉	D₄	1	2	yes	—
46	C₂×#41×C₁₉	D₄	1	2	yes	—
47	C₂×#41×C₁₉	Q₈	1	2	yes	—
48	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	2	no	—
53	C₂³×C₄×C₁₉	D₄	1	2	yes	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂³×Dic₁₉	—	2	1	no	—
56	C₂³×Dic₁₉	—	2	1	no	—
57	C₄×Q₈×C₁₉	—	2	4	no	—
58	C₄×Q₈×C₁₉	—	2	4	no	—
59	C₄×D₄×C₁₉	—	2	8	no	—
60	C₄×D₄×C₁₉	—	2	4	no	—
61	C₄×D₄×C₁₉	—	2	4	no	—
62	C₄×D₄×C₁₉	—	2	8	no	—
63	C₁₉×#117	—	2	4	no	—
64	C₁₉×#117	—	2	1	no	—
65	C₁₉×#117	—	2	1	no	—
66	C₁₉×#117	—	2	4	no	—
67	C₁₉×#117	C₂×C₄	1	2	yes	—
68	C₁₉×#117	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
76	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	—	2	1	no	—
84	C₂×C₄⋊Dic₁₉	—	2	1	no	—
85	C₂×C₄⋊Dic₁₉	—	2	1	no	—
86	C₂×C₄⋊Dic₁₉	—	2	1	no	—
87	C₂×C₄⋊Dic₁₉	—	2	1	no	—
88	C₂×C₄⋊Dic₁₉	—	2	1	no	—
89	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	complemented
90	C₂×C₄×Dic₁₉	—	2	1	no	—
91	C₂×C₄×Dic₁₉	—	2	1	no	—
92	C₂×C₄×Dic₁₉	—	2	1	no	—
93	C₂×C₄×Dic₁₉	—	2	1	no	—
94	C₂×C₄×Dic₁₉	—	2	1	no	—
95	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	complemented
96	C₂×#64520	—	2	1	no	—
97	C₂×#64520	—	2	1	no	—
98	C₂×#64520	—	2	1	no	—
99	C₂×#64520	—	2	1	no	—
100	C₂×#64520	—	2	1	no	—
101	C₂×#64520	—	2	1	no	—
102	C₂×#64520	—	2	1	no	—
103	C₂×#64520	—	2	1	no	—
104	C₂×#64520	—	2	1	no	—
105	C₂×#64520	—	2	1	no	—
106	C₂×#64520	C₂×C₄	1	2	yes	complemented
107	C₂×#64520	C₂×C₄	1	2	yes	complemented
108	C₂²×C₁₉⋊C₈	—	2	1	no	—
109	C₂²×C₁₉⋊C₈	—	2	1	no	—
110	#10597294	—	2	8	no	—
111	#10597292	—	2	4	no	—
112	#10597289	—	2	4	no	—
113	C₁₉⋊#95	—	4	4	no	—
114	C₂⁴×C₁₉	—	2	1	no	—
115	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
116	#41×C₁₉	—	2	2	no	—
117	#41×C₁₉	—	2	2	no	—
118	#41×C₁₉	—	2	2	no	—
119	#41×C₁₉	—	2	2	no	—
120	#41×C₁₉	—	2	2	no	—
121	#41×C₁₉	—	2	2	no	—
122	#41×C₁₉	—	2	2	no	—
123	#41×C₁₉	—	2	2	no	—
124	#41×C₁₉	—	2	2	no	—
125	#41×C₁₉	—	2	2	no	—
126	#41×C₁₉	—	2	2	no	—
127	#41×C₁₉	—	2	2	no	—
128	#41×C₁₉	C₄²	1	4	yes	—
129	#41×C₁₉	C₂²⋊C₄	1	4	yes	—
130	#41×C₁₉	C₄⋊C₄	1	4	yes	—
131	#41×C₁₉	C₄⋊C₄	1	4	yes	—
132	C₂×Q₈×C₁₉	—	2	1	no	—
133	C₂×Q₈×C₁₉	—	2	1	no	—
134	C₂×Q₈×C₁₉	—	2	1	no	—
135	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
137	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
138	C₂×D₄×C₁₉	—	2	2	no	—
139	C₂×D₄×C₁₉	—	2	2	no	—
140	C₂×D₄×C₁₉	—	2	2	no	—
141	C₂×D₄×C₁₉	—	2	2	no	—
142	C₂×D₄×C₁₉	—	2	2	no	—
143	C₂×D₄×C₁₉	—	2	2	no	—
144	C₂×D₄×C₁₉	—	2	1	no	—
145	C₂×D₄×C₁₉	—	2	1	no	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
148	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
149	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
150	C₂²×C₄×C₁₉	—	2	1	no	—
151	C₂²×C₄×C₁₉	—	2	2	no	—
152	C₂²×C₄×C₁₉	—	2	2	no	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	2	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	2	2	no	—
159	C₂²×C₄×C₁₉	—	2	1	no	—
160	C₂²×C₄×C₁₉	—	2	8	no	—
161	C₂²×C₄×C₁₉	—	2	2	no	—
162	C₂²×C₄×C₁₉	—	4	2	no	—
163	C₂²×C₄×C₁₉	—	4	2	no	—
164	C₂²×C₄×C₁₉	—	8	2	no	—
165	C₂²×C₄×C₁₉	—	8	2	no	—
166	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
167	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
177	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
178	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
179	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
180	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
181	C₂²×Dic₁₉	—	2	2	no	—
182	C₂²×Dic₁₉	—	2	2	no	—
183	C₂²×Dic₁₉	—	2	2	no	—
184	C₂²×Dic₁₉	—	2	2	no	—
185	C₂²×Dic₁₉	—	4	1	no	—
186	C₂²×Dic₁₉	—	4	1	no	—
187	C₂²×Dic₁₉	—	4	1	no	—
188	C₂²×Dic₁₉	—	4	1	no	—
189	C₂²×Dic₁₉	—	4	2	no	—
190	C₂²×Dic₁₉	—	4	2	no	—
191	C₂²×Dic₁₉	—	4	1	no	—
192	C₂²×Dic₁₉	—	4	1	no	—
193	C₄⋊C₄×C₁₉	—	2	8	no	—
194	C₄⋊C₄×C₁₉	—	2	2	no	—
195	C₄⋊C₄×C₁₉	—	2	2	no	—
196	C₄⋊C₄×C₁₉	—	2	2	no	—
197	C₄⋊C₄×C₁₉	—	2	1	no	—
198	C₄⋊C₄×C₁₉	—	2	2	no	—
199	C₄⋊C₄×C₁₉	—	2	1	no	—
200	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
201	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
202	C₂²⋊C₄×C₁₉	—	2	8	no	—
203	C₂²⋊C₄×C₁₉	—	2	2	no	—
204	C₂²⋊C₄×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	2	8	no	—
206	C₄²×C₁₉	—	2	2	no	—
207	C₄²×C₁₉	—	2	2	no	—
208	C₄⋊Dic₁₉	—	2	2	no	—
209	C₄⋊Dic₁₉	—	2	2	no	—
210	C₄⋊Dic₁₉	—	4	1	no	—
211	C₄⋊Dic₁₉	—	4	1	no	—
212	C₄×Dic₁₉	—	2	2	no	—
213	C₄×Dic₁₉	—	2	2	no	—
214	C₄×Dic₁₉	—	4	1	no	—
215	C₄×Dic₁₉	—	4	1	no	—
216	#64520	—	2	2	no	—
217	#64520	—	2	2	no	—
218	#64520	—	2	2	no	—
219	#64520	—	2	2	no	—
220	#64520	—	4	1	no	—
221	#64520	—	4	1	no	—
222	#64520	—	4	1	no	—
223	#64520	—	4	1	no	—
224	C₂×C₁₉⋊C₈	—	2	2	no	—
225	C₂×C₁₉⋊C₈	—	2	2	no	—
226	C₂×C₁₉⋊C₈	—	4	1	no	—
227	C₂×C₁₉⋊C₈	—	4	1	no	—
228	C₂×C₁₉⋊C₈	—	4	1	no	—
229	C₂×C₁₉⋊C₈	—	4	1	no	—
230	#10781	—	19	1	no	maximal, Sylow
231	C₂³×C₁₉	—	2	1	no	—
232	C₂³×C₁₉	—	2	1	no	—
233	C₂³×C₁₉	—	2	1	no	—
234	C₂³×C₁₉	—	2	1	no	—
235	C₂³×C₁₉	—	2	2	no	—
236	C₂³×C₁₉	—	2	2	no	—
237	C₂³×C₁₉	—	2	2	no	—
238	C₂³×C₁₉	—	4	1	no	—
239	C₂³×C₁₉	—	4	1	no	—
240	C₂³×C₁₉	—	4	1	no	—
241	C₂³×C₁₉	—	4	1	no	—
242	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
244	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
245	C₂³×C₁₉	#120	1	1	yes	characteristic
246	C₂³×C₁₉	#120	1	1	yes	characteristic
247	C₂³×C₁₉	#121	1	1	yes	characteristic
248	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
249	Q₈×C₁₉	—	2	2	no	—
250	Q₈×C₁₉	—	2	2	no	—
251	Q₈×C₁₉	—	2	2	no	—
252	Q₈×C₁₉	#95	1	4	yes	complemented
253	D₄×C₁₉	—	2	4	no	—
254	D₄×C₁₉	—	2	4	no	—
255	D₄×C₁₉	—	2	4	no	—
256	D₄×C₁₉	—	2	4	no	—
257	D₄×C₁₉	—	2	2	no	—
258	D₄×C₁₉	—	2	2	no	—
259	D₄×C₁₉	—	2	2	no	—
260	D₄×C₁₉	#95	1	4	yes	complemented
261	C₂×C₄×C₁₉	—	2	2	no	—
262	C₂×C₄×C₁₉	—	2	2	no	—
263	C₂×C₄×C₁₉	—	2	2	no	—
264	C₂×C₄×C₁₉	—	2	4	no	—
265	C₂×C₄×C₁₉	—	2	4	no	—
266	C₂×C₄×C₁₉	—	2	4	no	—
267	C₂×C₄×C₁₉	—	2	4	no	—
268	C₂×C₄×C₁₉	—	2	2	no	—
269	C₂×C₄×C₁₉	—	2	4	no	—
270	C₂×C₄×C₁₉	—	2	2	no	—
271	C₂×C₄×C₁₉	—	4	2	no	—
272	C₂×C₄×C₁₉	—	4	1	no	—
273	C₂×C₄×C₁₉	—	4	1	no	—
274	C₂×C₄×C₁₉	—	4	2	no	—
275	C₂×C₄×C₁₉	—	4	1	no	—
276	C₂×C₄×C₁₉	—	4	1	no	—
277	C₂×C₄×C₁₉	—	4	4	no	—
278	C₂×C₄×C₁₉	—	8	2	no	—
279	C₂×C₄×C₁₉	—	8	8	no	—
280	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
281	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
289	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
290	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
297	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
298	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
299	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
300	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
301	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
302	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
303	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
304	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
305	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
306	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
307	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
308	C₂×Dic₁₉	—	2	4	no	—
309	C₂×Dic₁₉	—	4	2	no	—
310	C₂×Dic₁₉	—	4	2	no	—
311	C₂×Dic₁₉	—	4	2	no	—
312	C₂×Dic₁₉	—	4	2	no	—
313	C₂×Dic₁₉	—	4	2	no	—
314	C₂×Dic₁₉	—	4	2	no	—
315	C₂×Dic₁₉	—	4	4	no	—
316	C₂×Dic₁₉	—	4	2	no	—
317	C₂×Dic₁₉	—	8	2	no	—
318	C₂×Dic₁₉	—	8	1	no	—
319	C₂×Dic₁₉	—	8	1	no	—
320	C₁₉⋊C₈	—	4	2	no	—
321	C₁₉⋊C₈	—	4	2	no	—
322	C₂×#520	D₁₉	1	1	yes	characteristic
323	C₂²×#104	—	19	1	no	—
324	C₂×#417	—	19	1	no	—
325	C₂×#343	—	19	1	no	—
326	#1736	—	19	1	no	—
327	C₂×#339	—	19	1	no	—
328	C₄⋊#95	—	19	1	no	—
329	C₂²×C₁₉	—	2	1	no	—
330	C₂²×C₁₉	—	2	1	no	—
331	C₂²×C₁₉	—	2	1	no	—
332	C₂²×C₁₉	—	2	1	no	—
333	C₂²×C₁₉	—	2	1	no	—
334	C₂²×C₁₉	—	2	1	no	—
335	C₂²×C₁₉	—	2	1	no	—
336	C₂²×C₁₉	—	2	1	no	—
337	C₂²×C₁₉	—	2	1	no	—
338	C₂²×C₁₉	—	2	1	no	—
339	C₂²×C₁₉	—	2	1	no	—
340	C₂²×C₁₉	—	2	1	no	—
341	C₂²×C₁₉	—	2	4	no	—
342	C₂²×C₁₉	—	4	2	no	—
343	C₂²×C₁₉	—	4	2	no	—
344	C₂²×C₁₉	—	4	2	no	—
345	C₂²×C₁₉	—	4	2	no	—
346	C₂²×C₁₉	—	4	2	no	—
347	C₂²×C₁₉	—	4	2	no	—
348	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
349	C₂²×C₁₉	#379	1	1	yes	characteristic
350	C₂²×C₁₉	#380	1	1	yes	characteristic
351	C₂²×C₁₉	#385	1	1	yes	characteristic
352	C₂²×C₁₉	#385	1	1	yes	characteristic
353	C₂²×C₁₉	#386	1	1	yes	characteristic
354	C₂²×C₁₉	#386	1	1	yes	characteristic
355	C₂²×C₁₉	#453	1	1	yes	characteristic
356	C₂²×C₁₉	#454	1	1	yes	characteristic
357	C₂²×C₁₉	#455	1	1	yes	characteristic
358	C₂²×C₁₉	#456	1	1	yes	characteristic
359	C₄×C₁₉	—	2	4	no	—
360	C₄×C₁₉	—	4	4	no	—
361	C₄×C₁₉	—	4	2	no	—
362	C₄×C₁₉	—	4	2	no	—
363	C₄×C₁₉	C₂×#95	1	1	yes	characteristic
364	C₄×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
365	C₄×C₁₉	#380	1	1	yes	characteristic
366	C₄×C₁₉	#381	1	1	yes	characteristic
367	C₄×C₁₉	#385	1	1	yes	characteristic
368	C₄×C₁₉	#385	1	1	yes	characteristic
369	C₄×C₁₉	#386	1	1	yes	characteristic
370	C₄×C₁₉	#386	1	1	yes	characteristic
371	Dic₁₉	—	4	4	no	—
372	Dic₁₉	—	8	2	no	—
373	C₂²×#41	C₂×D₁₉	1	1	yes	characteristic
374	C₂²×M₁₆	—	19	1	no	—
375	C₂²×M₁₆	—	19	1	no	—
376	#520	—	2	2	no	—
377	#520	—	2	2	no	—
378	#520	—	2	2	no	—
379	#520	Dic₁₉	1	4	yes	complemented
380	C₂×C₄×Q₈	—	2	1	no	—
381	C₂×C₄×D₄	—	2	1	no	—
382	C₂×C₄×D₄	—	2	2	no	—
383	C₂×#117	—	2	1	no	—
384	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
385	C₂²×C₄⋊C₄	—	2	1	no	—
386	C₂²×C₄⋊C₄	—	19	1	no	—
387	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
388	C₂²×C₄²	—	19	1	no	—
389	C₂×#104	—	19	4	no	—
390	C₂×#104	—	38	2	no	—
391	C₂×#104	—	38	2	no	—
392	#417	—	19	4	no	—
393	#417	—	38	2	no	—
394	C₂×#103	—	38	1	no	—
395	C₂×#102	—	38	1	no	—
396	C₂×#95	—	38	2	no	—
397	#343	—	38	2	no	—
398	#340	—	38	1	no	—
399	#340	—	38	1	no	—
400	#339	—	38	2	no	—
401	C₂×C₁₉	—	2	1	no	—
402	C₂×C₁₉	—	2	1	no	—
403	C₂×C₁₉	—	2	1	no	—
404	C₂×C₁₉	—	2	1	no	—
405	C₂×C₁₉	—	4	4	no	—
406	C₂×C₁₉	C₂²⋊#95	1	1	yes	characteristic
407	C₂×C₁₉	#1792	1	1	yes	characteristic
408	C₂×C₁₉	#1793	1	1	yes	characteristic
409	C₂×C₁₉	#1859	1	1	yes	characteristic
410	C₂×C₁₉	#1860	1	1	yes	characteristic
411	C₂×C₁₉	#1882	1	1	yes	characteristic
412	C₂×C₁₉	#1883	1	1	yes	characteristic
413	C₂×#41	—	2	1	no	—
414	C₂×#41	—	2	1	no	—
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	Dic₃₈	1	2	yes	—
420	C₂×#41	C₄×D₁₉	1	2	yes	—
421	C₂×#41	C₄×D₁₉	1	2	yes	—
422	C₂×#41	D₇₆	1	2	yes	—
423	C₂×#41	C₂×Dic₁₉	1	2	yes	—
424	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
425	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
426	C₂²×D₄	—	2	1	no	—
427	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
428	C₂³×C₄	—	2	1	no	—
429	C₂³×C₄	—	2	2	no	—
430	C₂³×C₄	—	38	1	no	—
431	C₂³×C₄	—	38	1	no	—
432	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
433	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
434	C₂×M₁₆	—	19	2	no	—
435	C₂×M₁₆	—	19	2	no	—
436	C₂×M₁₆	—	38	1	no	—
437	C₂×M₁₆	—	38	1	no	—
438	C₂×M₁₆	—	38	1	no	—
439	C₂×M₁₆	—	38	1	no	—
440	C₂×M₁₆	—	38	1	no	—
441	C₂×M₁₆	—	38	1	no	—
442	C₂×M₁₆	—	38	1	no	—
443	C₂×M₁₆	—	38	1	no	—
444	C₂×M₁₆	—	38	1	no	—
445	C₂×M₁₆	—	38	1	no	—
446	C₂²×C₈	—	38	1	no	—
447	C₂²×C₈	—	38	1	no	—
448	C₄×Q₈	—	2	4	no	—
449	C₄×Q₈	—	2	4	no	—
450	C₄×D₄	—	2	8	no	—
451	C₄×D₄	—	2	4	no	—
452	C₄×D₄	—	2	4	no	—
453	C₄×D₄	—	2	8	no	—
454	#117	—	2	4	no	—
455	#117	—	2	1	no	—
456	#117	—	2	1	no	—
457	#117	—	2	4	no	—
458	#117	C₂×Dic₁₉	1	2	yes	—
459	#117	C₂²⋊D₁₉	1	2	yes	—
460	C₂×C₄⋊C₄	—	2	2	no	—
461	C₂×C₄⋊C₄	—	2	4	no	—
462	C₂×C₄⋊C₄	—	2	1	no	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	2	1	no	—
466	C₂×C₄⋊C₄	—	2	4	no	—
467	C₂×C₄⋊C₄	—	19	2	no	—
468	C₂×C₄⋊C₄	—	38	1	no	—
469	C₂×C₄⋊C₄	—	38	1	no	—
470	C₂×C₄⋊C₄	—	38	1	no	—
471	C₂×C₄⋊C₄	—	38	1	no	—
472	C₂×C₄⋊C₄	—	38	1	no	—
473	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
474	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
475	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
476	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	—	2	2	no	—
478	C₂×C₂²⋊C₄	—	2	1	no	—
479	C₂×C₄²	—	2	2	no	—
480	C₂×C₄²	—	2	1	no	—
481	C₂×C₄²	—	19	2	no	—
482	C₂×C₄²	—	38	1	no	—
483	C₂×C₄²	—	38	1	no	—
484	C₂×C₄²	—	38	1	no	—
485	C₂×C₄²	—	38	1	no	—
486	C₂×C₄²	—	38	1	no	—
487	#104	—	38	8	no	—
488	#103	—	38	4	no	—
489	#102	—	38	4	no	—
490	#95	—	76	4	no	—
491	C₁₉	#10781	1	1	yes	characteristic, complemented, Sylow
492	C₂⁴	—	2	1	no	—
493	C₂⁴	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
494	#41	—	2	2	no	—
495	#41	—	2	2	no	—
496	#41	—	2	2	no	—
497	#41	—	2	2	no	—
498	#41	—	2	2	no	—
499	#41	—	2	2	no	—
500	#41	—	2	2	no	—
501	#41	—	2	2	no	—
502	#41	—	2	2	no	—
503	#41	—	2	2	no	—
504	#41	—	2	2	no	—
505	#41	—	2	2	no	—
506	#41	C₄×Dic₁₉	1	4	yes	—
507	#41	Dic₁₉⋊C₄	1	4	yes	—
508	#41	C₄⋊Dic₁₉	1	4	yes	—
509	#41	(C₂×D₁₉)⋊C₄	1	4	yes	—
510	C₂×Q₈	—	2	1	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
514	C₂×Q₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
515	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
516	C₂×D₄	—	2	2	no	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	2	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	2	1	no	—
523	C₂×D₄	—	2	1	no	—
524	C₂×D₄	—	2	1	no	—
525	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
526	C₂×D₄	(C₂×D₁₉)⋊C₄	1	2	yes	—
527	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	2	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	2	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	8	no	—
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	8	2	no	—
543	C₂²×C₄	—	8	2	no	—
544	C₂²×C₄	—	38	2	no	—
545	C₂²×C₄	—	38	2	no	—
546	C₂²×C₄	—	38	2	no	—
547	C₂²×C₄	—	38	2	no	—
548	C₂²×C₄	—	76	1	no	—
549	C₂²×C₄	—	76	1	no	—
550	C₂²×C₄	—	76	1	no	—
551	C₂²×C₄	—	76	1	no	—
552	C₂²×C₄	—	76	2	no	—
553	C₂²×C₄	—	76	2	no	—
554	C₂²×C₄	—	76	1	no	—
555	C₂²×C₄	—	76	1	no	—
556	C₂²×C₄	C₂²⋊Dic₁₉	1	4	yes	—
557	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
558	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
559	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
560	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
561	C₂²×C₄	#64541	1	1	yes	characteristic
562	C₂²×C₄	#64541	1	1	yes	characteristic
563	C₂²×C₄	#64541	1	1	yes	characteristic
564	C₂²×C₄	#64541	1	1	yes	characteristic
565	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
566	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
571	M₁₆	—	38	2	no	—
572	M₁₆	—	38	2	no	—
573	M₁₆	—	38	2	no	—
574	M₁₆	—	38	2	no	—
575	M₁₆	—	76	1	no	—
576	M₁₆	—	76	1	no	—
577	M₁₆	—	76	1	no	—
578	M₁₆	—	76	1	no	—
579	C₂×C₈	—	38	2	no	—
580	C₂×C₈	—	38	2	no	—
581	C₂×C₈	—	76	1	no	—
582	C₂×C₈	—	76	1	no	—
583	C₂×C₈	—	76	1	no	—
584	C₂×C₈	—	76	1	no	—
585	C₄⋊C₄	—	2	8	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	38	2	no	—
593	C₄⋊C₄	—	38	2	no	—
594	C₄⋊C₄	—	76	1	no	—
595	C₄⋊C₄	—	76	1	no	—
596	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
597	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₄²	—	2	8	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	38	2	no	—
605	C₄²	—	38	2	no	—
606	C₄²	—	76	1	no	—
607	C₄²	—	76	1	no	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	1	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	1	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	—	4	1	no	—
618	C₂³	—	4	1	no	—
619	C₂³	#10597370	1	1	yes	characteristic
620	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
621	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
622	C₂³	#10597376	1	1	yes	characteristic
623	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
624	C₂³	#10597399	1	1	yes	characteristic
625	C₂³	#10597399	1	1	yes	characteristic
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	C₁₉⋊#95	1	4	yes	complemented
630	D₄	—	2	4	no	—
631	D₄	—	2	4	no	—
632	D₄	—	2	4	no	—
633	D₄	—	2	4	no	—
634	D₄	—	2	2	no	—
635	D₄	—	2	2	no	—
636	D₄	—	2	2	no	—
637	D₄	C₁₉⋊#95	1	4	yes	complemented
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	4	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	2	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	—	8	2	no	—
656	C₂×C₄	—	8	8	no	—
657	C₂×C₄	—	38	4	no	—
658	C₂×C₄	—	76	2	no	—
659	C₂×C₄	—	76	2	no	—
660	C₂×C₄	—	76	2	no	—
661	C₂×C₄	—	76	2	no	—
662	C₂×C₄	—	76	2	no	—
663	C₂×C₄	—	76	2	no	—
664	C₂×C₄	—	76	4	no	—
665	C₂×C₄	—	76	2	no	—
666	C₂×C₄	—	152	2	no	—
667	C₂×C₄	—	152	1	no	—
668	C₂×C₄	—	152	1	no	—
669	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
670	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
671	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
672	C₂×C₄	#10597370	1	1	yes	characteristic
673	C₂×C₄	#10597370	1	1	yes	characteristic
674	C₂×C₄	#10597370	1	1	yes	characteristic
675	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
676	C₂×C₄	#10597372	1	1	yes	characteristic
677	C₂×C₄	#10597372	1	1	yes	characteristic
678	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
679	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
680	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
681	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
682	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
683	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
684	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
685	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
686	C₂×C₄	#10597375	1	1	yes	characteristic
687	C₂×C₄	#10597375	1	1	yes	characteristic
688	C₂×C₄	#10597375	1	1	yes	characteristic
689	C₂×C₄	#10597375	1	1	yes	characteristic
690	C₂×C₄	#10597376	1	1	yes	characteristic
691	C₂×C₄	#10597376	1	1	yes	characteristic
692	C₂×C₄	#10597376	1	1	yes	characteristic
693	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
694	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
695	C₂×C₄	#10597399	1	1	yes	characteristic
696	C₂×C₄	#10597399	1	1	yes	characteristic
697	C₈	—	76	2	no	—
698	C₈	—	76	2	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	1	no	—
710	C₂²	—	2	1	no	—
711	C₂²	—	2	4	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	2	no	—
714	C₂²	—	4	2	no	—
715	C₂²	—	4	2	no	—
716	C₂²	—	4	2	no	—
717	C₂²	—	4	2	no	—
718	C₂²	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
719	C₂²	#11926400	1	1	yes	characteristic
720	C₂²	#11926404	1	1	yes	characteristic
721	C₂²	#11926417	1	1	yes	characteristic
722	C₂²	#11926417	1	1	yes	characteristic
723	C₂²	#11926423	1	1	yes	characteristic
724	C₂²	#11926423	1	1	yes	characteristic
725	C₂²	#11926712	1	1	yes	characteristic
726	C₂²	#11926717	1	1	yes	characteristic
727	C₂²	#11926722	1	1	yes	characteristic
728	C₂²	#11926727	1	1	yes	characteristic
729	C₄	—	2	4	no	—
730	C₄	—	4	4	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	76	4	no	—
734	C₄	—	152	2	no	—
735	C₄	C₂×C₁₉⋊#95	1	1	yes	characteristic
736	C₄	C₄×C₂²⋊Dic₁₉	1	1	yes	characteristic
737	C₄	#11926404	1	1	yes	characteristic
738	C₄	#11926407	1	1	yes	characteristic
739	C₄	#11926417	1	1	yes	characteristic
740	C₄	#11926417	1	1	yes	characteristic
741	C₄	#11926423	1	1	yes	characteristic
742	C₄	#11926423	1	1	yes	characteristic
743	C₂	—	2	1	no	—
744	C₂	—	2	1	no	—
745	C₂	—	2	1	no	—
746	C₂	—	2	1	no	—
747	C₂	—	4	4	no	—
748	C₂	#14561858	1	1	yes	characteristic
749	C₂	#14563589	1	1	yes	characteristic
750	C₂	#14563594	1	1	yes	characteristic
751	C₂	#14563861	1	1	yes	characteristic
752	C₂	#14563868	1	1	yes	characteristic
753	C₂	#14564004	1	1	yes	characteristic
754	C₂	#14564011	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#520	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×#41×C₁₉	C₂²
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#520	D₁₉
hypocenter	C₁₉	#10781
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#520

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₂×#11926313	C₂	semidirect
4. #14563356	C₂	semidirect
5. C₂×#11926303	C₂	semidirect
6. #14561864	C₂	semidirect
14. C₂×#10597294	C₄	semidirect
16. #11926545	C₄	semidirect
28. C₁₉×#520	C₄	semidirect
89. C₂×C₄⋊Dic₁₉	C₂×C₄	semidirect
95. C₂×C₄×Dic₁₉	C₂×C₄	semidirect
106. C₂×#64520	C₂×C₄	semidirect
107. C₂×#64520	C₂×C₄	semidirect
252. Q₈×C₁₉	#95	semidirect
260. D₄×C₁₉	#95	semidirect
379. #520	Dic₁₉	semidirect
491. C₁₉	#10781	semidirect
629. Q₈	C₁₉⋊#95	semidirect
637. D₄	C₁₉⋊#95	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#10597294	2
C₂×#11926545	2
C₂×#11926313	2
#14563356	2
C₂×#11926303	2
#14561864	2
C₂×C₁₉×#520	2
#10781	19